Starting from rest, a 4.4 kg block slides 3.5 m down a rough 22.3o incline in 2.4 seconds. Determine the energy lost due to friction. (Hint: find the final kinetic energy and subtract that from the work done by gravity.)
Enter your answer here: J
Your hint tells you how to do it.
The final velocity is twice the average velocity of 3.5/2.4 m/s, which would be
Vfinal = 2.92 m/s
Energy lost = M g H - (1/2) M Vfinal^2/2
You do not need to use the slope of the incline to get the answer. You COULD use it to get the kinetic friction coefficient.
average velocity= distance/time=3.5/2.4 m/s
so final velocity= 2*averagevelociyt
and KEfinal= 1/2 m vf^2
height of ramp= 3.5sin22.3
mgh=you figure.
energy from friction= mgh- KEfinal
To determine the energy lost due to friction, we need to follow these steps:
1. Calculate the final kinetic energy of the block:
- The block starts from rest, so its initial kinetic energy (K_i) is zero.
- The final velocity (v_f) can be calculated using the equation of motion: v_f = v_i + a*t, where v_i is the initial velocity (which is zero), a is the acceleration, and t is the time.
- The acceleration (a) can be calculated using the equation: a = g*sin(theta), where g is the acceleration due to gravity and theta is the angle of the incline.
- Substitute the given values: g = 9.8 m/s^2 (approximate value), sin(theta) = sin(22.3) = 0.3746.
- Now, calculate the acceleration: a = 9.8 m/s^2 * 0.3746 = 3.6628 m/s^2 (approximate value).
- Substitute the values of v_i, a, and t into the equation v_f = v_i + a*t: v_f = 0 + 3.6628 m/s^2 * 2.4 s = 8.7931 m/s (approximate value).
- The final kinetic energy (K_f) can be calculated using the equation: K_f = (1/2) * m * v_f^2, where m is the mass of the block.
- Substitute the given values: m = 4.4 kg, v_f = 8.7931 m/s.
- Now, calculate K_f: K_f = (1/2) * 4.4 kg * (8.7931 m/s)^2 = 170.2081 J (approximate value).
2. Calculate the work done by gravity:
- The work done by gravity is given by the equation: W = m * g * d * cos(theta), where d is the distance traveled along the incline.
- Substitute the given values: m = 4.4 kg, g = 9.8 m/s^2 (approximate value), d = 3.5 m, cos(theta) = cos(22.3) = 0.9272.
- Now, calculate the work done by gravity: W = 4.4 kg * 9.8 m/s^2 * 3.5 m * 0.9272 = 144.2612 J (approximate value).
3. Determine the energy lost due to friction:
- The energy lost due to friction is the difference between the final kinetic energy and the work done by gravity.
- Subtract the work done by gravity (144.2612 J) from the final kinetic energy (170.2081 J) to find the energy lost due to friction.
- Energy lost due to friction = K_f - W = 170.2081 J - 144.2612 J = 25.9469 J (approximate value).
Therefore, the energy lost due to friction is approximately 25.9469 J.